The e-MANTIS emulator: Fast and accurate predictions of the halo mass function in f(R)CDM and wCDM cosmologies

¹ Laboratoire Univers et Théories, Université Paris Cité, Observatoire de Paris, Université PSL, CNRS, 92190 Meudon, France
² Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal, 4, 20018, Donostia-San Sebastián, Gipuzkoa, Spain
³ Sorbonne Université, CNRS, UMR 7095, Institut d’Astrophysique de Paris, 98 bis bd Arago, 75014 Paris, France
⁴ Institut universitaire de France (IUF), France

^★ Corresponding author; inigo.saez-casares@obspm.fr

Received: 31 March 2024
Accepted: 30 September 2024

Abstract

Aims. In this work, we present a novel emulator of the halo mass function (HMF), which we implemented in the framework of the e-MANTIS emulator of f(R) gravity models. We also extended e-MANTIS to cover a larger cosmological parameter space and to include models of dark energy with a constant equation of state wCDM.

Methods. We used a Latin hypercube sampling of the wCDM and f(R)CDM cosmological parameter spaces, over a wide range, and carried out a large suite of more than 10 000 N-body simulations with a different volume, mass resolution, and random phase for the initial conditions. For each simulation in the suite, we generated halo catalogues using the friends-of-friends (FoF) halo finder, as well as the spherical overdensity (SO) algorithm for different overdensity thresholds (200, 500, and 1000 times the critical density). We decomposed the corresponding HMFs on a B-spline basis, while adopting a minimal set of assumptions on their shape. We used this decomposition to train an emulator based on Gaussian processes.

Results. The resulting emulator is able to predict the HMF for redshifts ≤1.5 and for halo masses M_h ≥ 10¹³ h⁻¹ M_⊙. The typical HMF errors for SO haloes with ∆ = 200c at ɀ = 0 in wCDM (respectively f(R)CDM) are of the order of ϵ₀ ≃ 1.5% (ϵ₀ ≃ 4%) up to a transition mass M_t ≃ 2 ⋅ 10¹⁴ h⁻¹ M_⊙ (M_t ≃ 6 ⋅ 10¹³ h⁻¹ M_⊙). For larger masses, the errors are dominated by the shot noise and scale as ϵ₀ ⋅ (M_h/M_t)^α with α ≃ 0.9 (α ≃ 0.4) up to M_h ~ 10¹⁵ h⁻¹ M_⊙. Independently of this general trend, the emulator is able to provide an estimation of its own error as a function of the cosmological parameters, halo mass, and redshift. We have performed an extensive comparison against analytical parametrizations and shown that e-MANTIS is able to better capture the cosmological dependence of the HMF, while being complementary to other existing emulators.

Conclusions. The e-MANTIS emulator, which is publicly available, can be used to obtain fast and accurate predictions of the HMF in the f(R)CDM and wCDM non-standard cosmological models. As such, it represents a useful theoretical tool to constrain the nature of dark energy using data from galaxy cluster surveys.